Two sound waves having displacements \(\mathrm{x}_1=2 \sin (1000 \pi \mathrm{t})\) and \(\mathrm{x}_2=3 \sin (1006 \pi \mathrm{t})\), when interfere, produce

Given,
\(\begin{aligned}
& \mathrm{X}_1=2 \sin (1000 \pi \mathrm{t}) \\
& \mathrm{X}_2=3 \sin (1006 \pi \mathrm{t})
\end{aligned}\)
Comparing with standard equation, \(\mathrm{x}=\mathrm{A} \sin \omega \mathrm{t}\)
\(\begin{aligned}
& \omega_1=1000 \pi, \omega_2=1006 \pi ...(i)\\
& \mathrm{~A}_1=2, \mathrm{~A}_2=3 ...(ii)\\
& \therefore \quad \mathrm{f}_1=\frac{\omega_1}{2 \pi}=\frac{1000 \pi}{2 \pi}=500 \mathrm{~Hz} ...[From(i)]\\
& \mathrm{f}_2=\frac{\omega_2}{2 \pi}=\frac{1006 \pi}{2 \pi}=503 \mathrm{~Hz}
...[From(ii)]\end{aligned}\)
\(\therefore \quad\) Beat frequency \(=503-500=3\) beats/second Intensity \(\propto \mathrm{A}_{\text {max }}^2\)
\(\mathrm{A}_{\max }=\mathrm{A}_1+\mathrm{A}_2=2+3=5\) units
...[From(ii)]
Intensity \(=(5)^2=25\) units